﻿Temperature is measured in both Celsius and Fahrenheit degrees. These two systems are of course related: the \(Fahrenheit\) temperature is obtained by adding 32 to 9/5 of the \(Celsius\) temperature. In the following questions, let \(C\) represent the Celsius temperature and \(F\) the Fahrenheit temperature.

(a) Write an equation that expresses \(F\) in terms of \(C\).

(b) Use this equation to find the value of \(F\) that corresponds to \(C=20\).

(c) On the Celsius scale, water freezes at \(0^{\mathrm{o}}\) and boils at \(100^{\mathrm{o}}\) Use your formula to find the corresponding temperatures on the Fahrenheit scale. Do you recognize your answers?

(d) A quick way to get an approximate Fahrenheit temperature from a Celsius temperature is to double the Celsius temperature and add 30. Explain why this is a good approximation. Convert \(23^{\mathrm{o}}\) Celsius the quick way. What is the difference between your answer and the correct value? For what Celsius temperature does the quick way give the correct value?

﻿Temperature is measured in both Celsius and Fahrenheit degrees. These two systems are of course related: the \(Fahrenheit\) temperature is obtained by adding 32 to 9/5 of the \(Celsius\) temperature. In the following questions, let \(C\) represent the Celsius temperature and \(F\) the Fahrenheit temperature.

(a) Write an equation that expresses \(F\) in terms of \(C\).

(b) Use this equation to find the value of \(F\) that corresponds to \(C=20\).

(c) On the Celsius scale, water freezes at \(0^{\mathrm{o}}\) and boils at \(100^{\mathrm{o}}\) Use your formula to find the corresponding temperatures on the Fahrenheit scale. Do you recognize your answers?

(d) A quick way to get an approximate Fahrenheit temperature from a Celsius temperature is to double the Celsius temperature and add 30. Explain why this is a good approximation. Convert \(23^{\mathrm{o}}\) Celsius the quick way. What is the difference between your answer and the correct value? For what Celsius temperature does the quick way give the correct value?

Because \(12x^{2}+5x^{2}\) is equivalent to \(17x^{2}\), the expressions \(12x^{2}\) and \(5x^{2}\) are called \({\it like~terms}\). Explain. Why are \(12x^{2}\) and \(5x\) called \({\it unlike~terms}\)? Are \(3ab\) and 11ab like terms? Explain. Are \(12x^{2}\) and \(5y^{2}\) like terms? Explain. Are \(12x^{2}\) and \(12x\) like terms? Explain.

Because \(12x^{2}+5x^{2}\) is equivalent to \(17x^{2}\), the expressions \(12x^{2}\) and \(5x^{2}\) are called \({\it like~terms}\). Explain. Why are \(12x^{2}\) and \(5x\) called \({\it unlike~terms}\)? Are \(3ab\) and 11ab like terms? Explain. Are \(12x^{2}\) and \(5y^{2}\) like terms? Explain. Are \(12x^{2}\) and \(12x\) like terms? Explain.

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection… (more)

(a) By completing the table of values, draw the lines y = 2x + 3 and x = 1 - 2y on the grid.
(b) Do the equations y = 2x + 3 and x = 1 - 2y have one common solution, no common solutions, or infinitely many common solutions? Explain how you know.
(c) Draw a straight line on the grid that has no common solutions with the line y = 2x + 3. What is the equation of your new line? Explain your answer.

(a) By completing the table of values, draw the lines y = 2x + 3 and x = 1 - 2y on the grid.
(b) Do the equations y = 2x + 3 and x = 1 - 2y have one common solution, no common solutions, or infinitely many common solutions? Explain how you know.
(c) Draw a straight line on the grid that has no common solutions with the line y = 2x + 3. What is the equation of your new line? Explain your answer.

(a) By completing the table of values, draw the lines y = 2x + 2 and x = 4 - 2y on the grid.
(b) Do the equations y = 2x + 2 and x = 4 - 2y have one common solution, no common solutions, or infinitely many common solutions? Explain how you know.
(c) Draw a straight line on the grid that has no common solutions with the line y = 2x + 2. What is the equation of your new line? Explain your answer.

(a) By completing the table of values, draw the lines y = 2x + 2 and x = 4 - 2y on the grid.
(b) Do the equations y = 2x + 2 and x = 4 - 2y have one common solution, no common solutions, or infinitely many common solutions? Explain how you know.
(c) Draw a straight line on the grid that has no common solutions with the line y = 2x + 2. What is the equation of your new line? Explain your answer.

Randy and Sandy have a total of 20 books between them. After Sandy loses three by leaving them on the bus, and some birthday gifts double Randy's collection, their total increases to 30 books. How many books did each have before these changes?

Randy and Sandy have a total of 20 books between them. After Sandy loses three by leaving them on the bus, and some birthday gifts double Randy's collection, their total increases to 30 books. How many books did each have before these changes?

Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine… (more)

Wale and Nicki Minaj are about to record an album together. They have a choice between two recording studios. One studio charges a $50 flat fee plus $2 per minute. The second charges a $20 flat fee plus $4 per minute. Wale thinks they should go with the second studio. Nicki Minaj thinks they should go with the first. For what numbers of minutes would each studio make sense? Use equations and a graph to justify your response.

Wale and Nicki Minaj are about to record an album together. They have a choice between two recording studios. One studio charges a $50 flat fee plus $2 per minute. The second charges a $20 flat fee plus $4 per minute. Wale thinks they should go with the second studio. Nicki Minaj thinks they should go with the first. For what numbers of minutes would each studio make sense? Use equations and a graph to justify your response.

Kimi and Jordan are both working during the summer to earn money in addition to their weekly allowances, and they are saving all their money. Kimi earns $9 an hour at her job, and her allowance is $8 per week. Jordan earns $7.50 an hour, and his allowance is $16 per week.

(a) Complete the table below:(b) Write an equation that can be used to calculate the total of Kimi's allowance and job earnings at the end of one week given the number of hours she works.(c) Write an equation that can be used to calculate the total of Jordan's allowance and job earnings at the end of one week given the number of hours he works.(d) Sketch the graphs of your two equations on a pair of axes.(e) Jordan wonders who will save more money in one week if they both work the same number of hours. Write an answer for him.

Kimi and Jordan are both working during the summer to earn money in addition to their weekly allowances, and they are saving all their money. Kimi earns $9 an hour at her job, and her allowance is $8 per week. Jordan earns $7.50 an hour, and his allowance is $16 per week.

(a) Complete the table below:(b) Write an equation that can be used to calculate the total of Kimi's allowance and job earnings at the end of one week given the number of hours she works.(c) Write an equation that can be used to calculate the total of Jordan's allowance and job earnings at the end of one week given the number of hours he works.(d) Sketch the graphs of your two equations on a pair of axes.(e) Jordan wonders who will save more money in one week if they both work the same number of hours. Write an answer for him.

Cee Lo Green and Rihanna are both on Twitter. Cee Lo Green has 125,000 followers with 500 joining everyday. Rihanna has 97,000 followers with 1,200 joining everyday. How long until Rihanna has more Twitter followers than Cee Lo Green? Write equations, make a graph, and solve the system to provide a precise answer.

Cee Lo Green and Rihanna are both on Twitter. Cee Lo Green has 125,000 followers with 500 joining everyday. Rihanna has 97,000 followers with 1,200 joining everyday. How long until Rihanna has more Twitter followers than Cee Lo Green? Write equations, make a graph, and solve the system to provide a precise answer.

You work for a video streaming company that has two monthly plans to choose from.
Plan 1: A flat rate of $7 per month plus $2.50 per video viewed.
Plan 2: $4 per video viewed.
(a) What type of functions model this situation? Explain how you know.
(b) Define variables that make sense in the context, and then write an equation for each plan with cost as a function of videos viewed.
(c) How much would 3 videos in a month cost for each plan? 5 videos?
(d) Compare the two plans and explain what advice you would give to a customer trying to decide which plan is best for them, based on their viewing habits.

You work for a video streaming company that has two monthly plans to choose from.
Plan 1: A flat rate of $7 per month plus $2.50 per video viewed.
Plan 2: $4 per video viewed.
(a) What type of functions model this situation? Explain how you know.
(b) Define variables that make sense in the context, and then write an equation for each plan with cost as a function of videos viewed.
(c) How much would 3 videos in a month cost for each plan? 5 videos?
(d) Compare the two plans and explain what advice you would give to a customer trying to decide which plan is best for them, based on their viewing habits.